Electromagnetic Localization 6-DoF Pose Estimation with TGNet-Guided Initial Value Refinement

High-precision electromagnetic localization shows great promise for applications in medical treatment, embodied intelligence, entertainment, and gaming. However, six-degree-of-freedom (6-DoF) coil pose estimation is essentially a highly nonlinear inverse problem. Numerical iterative solvers, such as the Levenberg–Marquardt (LM) algorithm, are sensitive to poor initial guesses and prone to getting trapped in local optima. This limitation has become a major bottleneck for improving the accuracy and robustness of electromagnetic localization systems. To address this problem, we propose a network termed TGNet (Transmitter Geometry-guided Network) that provides reliable initial guesses for the iterative solver. The network mainly consists of three parts: (i) a dual-branch module that encodes the spatial distribution of the transmitting coil as physical priors, thereby narrowing the ambiguous solution space and effectively mitigating pose ambiguity arising from multiple local extrema; (ii) a decoupled regression head that estimates the coil’s 6-DoF position and orientation independently, reducing cross-coupling complexity; and (iii) a numerical simulation-based data generation strategy that produces large-scale datasets of magnetic field measurements paired with ground-truth 6-DoF poses for fully supervised training, circumventing the difficulty of collecting real-world labeled data. Using TGNet predictions as initial guesses for the LM algorithm, we achieved average position and orientation errors of 1.5 mm and 0.6°, respectively, in real localization experiments. In contrast, using random data as initial guesses for the LM algorithm, the average position and orientation errors were 31.1 mm and 7.9°, confirming that the proposed initialization improves accuracy. First, TGNet reliably avoids local minima, as the LM algorithm converges at all test points in the localization space. Second, TGNet reduces the iteration counts of the LM algorithm, decreasing them from 39 to 14. Overall, TGNet provides a robust and efficient solution for high-performance electromagnetic localization.